A083895 Number of divisors of n with largest digit = 8 (base 10).

0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 1, 0, 1, 0, 2, 1, 1, 1, 2, 1, 1, 1, 2, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 1, 0

Offset

1,48

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Formula

a(n) = A000005(n) - A083888(n) - A083889(n) - A083890(n) - A083891(n) - A083892(n) - A083893(n) - A083894(n) - A083896(n) = A083903(n) - A083902(n).

Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = Sum_{k>=1} 1/A283611(k) = 11.62909500243165896645... . - Amiram Eldar, Jan 04 2024

Example

n=72, 2 of the 12 divisors of 72 have largest digit =8: {8,18}, therefore a(72)=2.

Maple

f:= proc(n) nops(select(t -> max(convert(t, base, 10))=d, numtheory:-divisors(n))) end proc:
d:= 8:
map(f, [$1..200]); # Robert Israel, Oct 06 2019

Mathematica

With[{k = 8}, Array[DivisorSum[#, 1 &, And[#[[k]] > 0, Total@ #[[k + 1 ;; 9]] == 0] &@ DigitCount[#] &] &, 105]] (* Michael De Vlieger, Oct 06 2019 *)

Crossrefs

Cf. A054055, A000005, A083903, A083888, A083889, A083890, A083891, A083892, A083893, A083894, A083896, A283611.

Sequence in context: A127268 A252459 A083918 * A093488 A085858 A188172

Adjacent sequences: A083892 A083893 A083894 * A083896 A083897 A083898

Keyword

nonn,base

Author

Reinhard Zumkeller, May 08 2003

Status

approved